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JEE Main & Advanced Mathematics Differentiation Question Bank Self Evaluation Test - Limits and Derivatives

  • question_answer
    Let \[f(x)=4\] and \[f'(x)=4.\]Then \[\underset{x\to 2}{\mathop{\lim }}\,\frac{xf(2)-2f(x)}{x-2}\] is given by

    A) 2

    B) -2

    C) -4

    D) 3

    Correct Answer: C

    Solution :

    [c] We have, \[\underset{x\to 2}{\mathop{\lim }}\,\frac{xf(2)-2f(x)}{x-2}\,\,\,\,\,\,\,\,\,\left( \frac{0}{0} \right)\] By applying ?L? Hospital rule, we get \[=\underset{x\to 2}{\mathop{\lim }}\,f(2)-2f'(x)=f(2)-2f'(2)\] \[=4-2\times 4=-4.\]


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